What is the speed of the train ?

**I.** The train crosses $300$ metres long platform in $21$ seconds.

**II.** The train crosses another stationary train of equal length in $19\frac{1}{2}$ seconds.

**III.** The train crosses a signal pole in $9\frac{3}{4}$ seconds.

**Answer:**

Option B**Explanation:**

Let the speed of the train be $x$ m/sec.

Time taken to cross a platform = (Length of train + Length of platform) / Speed of the train

Time taken by the train to cross a stationary train = (Sum of the lengths of the train) / Speed of moving train

Time taken to cross a signal pole = Length of train / Speed of train

**I** gives, $21=\frac{(l+300)}{x}$; **II** gives, $\frac{39}{2}$ $=\frac{2l}{x}$; **III** gives, $\frac{39}{4}$ $=\frac{l}{x}$

Thus, (I and II) or (I and III) give $x$.

$\therefore$ Correct answer is **(B)**.